Adversarial Intelligenceurn:uuid:0f7692d6-fe5b-4854-96ea-2c9a50c527b12018-11-13T00:00:00-07:00Wouter M. KoolenBounded Excess Risk for AdaHedgehttp://blog.wouterkoolen.info/2018-11-132018-11-13T00:00:00-07:00
We show that AdaHedge has constant excess risk (aka pseudo-regret) for nice stochastic cases.
The Value of Random Game Treeshttp://blog.wouterkoolen.info/2018-10-242018-10-24T00:00:00-07:00
We look at an intuitive generative model for game trees. We compute the distribution of the value of the root node, and see how it concentrates with the depth.
Solving Two-part Metal Puzzles: Theory and Practicehttp://blog.wouterkoolen.info/2018-09-292018-09-29T00:00:00-07:00
A brief look at two metal take-me-apart puzzles.
A Dynamical System view of some Exponential Updatehttp://blog.wouterkoolen.info/2018-06-112018-06-11T00:00:00-07:00
We consider a natural mapping from the simplex to itself, similar to but different from the well-known exponential weights scheme. We investigate the limit behaviour when iterating this mapping.
Conference on Learning Theory (COLT) Proceedingshttp://blog.wouterkoolen.info/2018-02-212018-02-21T00:00:00-07:00
The proceedings of the Conference On Learning Theory (COLT) 2010 are now online again.
Conference on Learning Theory (COLT) Video Archiveshttp://blog.wouterkoolen.info/2017-09-152017-09-15T00:00:00-07:00
The videos of the 2017 Conference On Learning Theory (COLT) are now online.
Bernoulli is Sub-Gaussianhttp://blog.wouterkoolen.info/2017-09-082017-09-08T00:00:00-07:00
We show that any Bernoulli random variable is sub-Gaussian with variance factor $\frac{1}{4}$.
A Quick and Dirty Finite Time Law of the Iterated Logarithm Resulthttp://blog.wouterkoolen.info/2017-04-262017-04-26T00:00:00-07:00
The Law of the Iterated Logarithm is an asymptotic uniform deviation bound.
We prove a finite time version using martingale arguments.
Visualisation of Conformal Mappingshttp://blog.wouterkoolen.info/2017-03-202017-03-20T00:00:00-07:00
A visualisation of conformal mappings.
Rendering with Droste Effectshttp://blog.wouterkoolen.info/2017-03-112017-03-11T00:00:00-07:00
A Droste image contains a smaller copy of itself. We look at how to render such images.
The Advantage of Full AdaGradhttp://blog.wouterkoolen.info/2017-01-212017-01-21T00:00:00-07:00
AdaGrad, an adaptive version of Online Gradient Descent, is often used in its diagonal version. In this post we take a look at the full matrix version to understand the benefit of its additional adaptive power.
Matrix iProd and Matrix Squinthttp://blog.wouterkoolen.info/2016-11-102016-11-10T00:00:00-07:00
We look at extending two recent adaptive online learning strategies, iProd and Squint, to the matrix Hedge setting. The extension is straightforward up to a point, but we end with a nice open problem.
AdaFTRLhttp://blog.wouterkoolen.info/2016-10-312016-10-31T00:00:00-07:00
We analyse AdaFTRL from the AdaHedge perspective.
Exploiting Curvature Using Exponential Weightshttp://blog.wouterkoolen.info/2016-09-062016-09-06T00:00:00-07:00
We show how Exponential Weights applies uniformly to convex losses, strongly convex losses and exp-concave losses.
A Tractable Bound for Simple Power Inequalitieshttp://blog.wouterkoolen.info/2016-09-012016-09-01T00:00:00-07:00
We study a simple type of power inequality that pops up in the analysis of learning algorithms. The inequality has no general analytic solution, and we find a tractable bound.
Visualising The Escort Probability Maphttp://blog.wouterkoolen.info/2016-08-112016-08-11T00:00:00-07:00
A simple visualisation of the escort probability map.
The Dual of the von Neumann Relative Entropyhttp://blog.wouterkoolen.info/2016-04-112016-04-11T00:00:00-07:00
We compute two duals of the von Neumann relative entropy between PSD matrices.
Gradient Descent as Exponential Weightshttp://blog.wouterkoolen.info/2016-02-212016-02-21T00:00:00-07:00
We regard gradient descent as an instance of exponential weights.
The GADDAGhttp://blog.wouterkoolen.info/2016-02-012016-02-01T00:00:00-07:00
We have a look at the GADDAG data structure.
The Bregman Divergence Generated by the Absolute Value Functionhttp://blog.wouterkoolen.info/2016-01-312016-01-31T00:00:00-07:00
We look at the Bregman divergence generated by the prototypical non-differentiable convex function.
Mixability Gap Boundshttp://blog.wouterkoolen.info/2016-01-132016-01-13T00:00:00-07:00
A collection of bounds on the mixability gap.
An Upper Bound on the Learning Rate for IID Datahttp://blog.wouterkoolen.info/2015-12-052015-12-05T00:00:00-07:00
We obtain an upper bound on the learning rate for convergence of the Hedge posterior in a simple iid data scenario.
Implementing Squinthttp://blog.wouterkoolen.info/2015-11-292015-11-29T00:00:00-07:00
We look at some tricks and considerations that came up during my implementation of Squint.
Tight Diagonal Upper Bounds on Dyadshttp://blog.wouterkoolen.info/2015-11-192015-11-19T00:00:00-07:00
We look at bounding a symmetric rank one matrix from above by a diagonal matrix.
Minimax on the Ballhttp://blog.wouterkoolen.info/2015-09-292015-09-29T00:00:00-07:00
We compare two minimax strategies on the ball.
Colliding Ballshttp://blog.wouterkoolen.info/2015-09-212015-09-21T00:00:00-07:00
Videos from my Newtonian collision simulator
Concave-convex vs Convex-convexhttp://blog.wouterkoolen.info/2015-09-082015-09-08T00:00:00-07:00
We look at a simple quadratic minimax problem on the Euclidean sphere, and consider what happens when it flips from convex to concave.
The Relative Entropy Bound for Squinthttp://blog.wouterkoolen.info/2015-08-132015-08-13T00:00:00-07:00
We derive the relative entropy version of the second-order quantile regret bound for Squint.
The Hedge Algorithm in Continuous Timehttp://blog.wouterkoolen.info/2015-05-252015-05-25T00:00:00-07:00
We look at the Hedge algorithm in a version of continuous time.
Exchangeable vs Mixture of IID for a Pair of Binary Outcomeshttp://blog.wouterkoolen.info/2015-05-222015-05-22T00:00:00-07:00
We determine which exchangeable distributions are mixtures of IID in the simple case of two binary outcomes.
Unknown Gameshttp://blog.wouterkoolen.info/2015-05-132015-05-13T00:00:00-07:00
We investigate what happens to simple matrix games and their solutions if we either randomly or strategically choose between two games.
Convex Duality Illustratedhttp://blog.wouterkoolen.info/2015-03-292015-03-29T00:00:00-07:00
Convex duality is an important tool in machine learning. Here I present an insightful arrangement of the graphs of a convex function, its dual and their derivatives.
Differentiability of Compositionshttp://blog.wouterkoolen.info/2015-03-082015-03-08T00:00:00-07:00
A composition of differentiable functions can be non-differentiable.
Close to the Perfect Expert, now Without Outcomeshttp://blog.wouterkoolen.info/2015-02-222015-02-22T00:00:00-07:00
We look at one of the simplest online learning problems: making decisions in the presence of a perfect expert. We derive a non-uniform regret bound.
Bimatrix Gameshttp://blog.wouterkoolen.info/2015-02-012015-02-01T00:00:00-07:00
We show that any two-player zero-sum bimatrix game has a saddle point where both players randomise over the same number of strategies.